DE102020210081A1 - Device and computer-implemented method for operating a fuel cell system - Google Patents

Abstract

Device and computer-implemented method for operating a fuel cell system, wherein at least one control variable (u_req) is specified for control of the fuel cell system, being set as a function of the at least one control variable (u_req) or as a function of at least one for the at least one control variable (u_req(t)). Control variable (u_act, u_pred) with a model (102) a prediction (y_pred, dy_pred) of a variable (y_mes, dy) of the fuel cell system is determined, and depending on the variable (y_mes, dy) and the prediction (y_pred, dy_pred) the variable (y_mes, dy) at least one parameter (P) of the model (102) is determined, depending on a measure of an uncertainty (h(u_req)) for the prediction (y_pred, dy_pred) of the variable (y_mes, dy) the model (102) determines the at least one specified control variable (u_req) for which the measure of the uncertainty (h(u_req)) satisfies a condition.

Description

State of the art

The invention relates to a device and a computer-implemented method for operating a fuel cell system.

A fuel cell system represents an overall system that includes a large number of subsystems. The fuel cell system includes one or more fuel cell stacks and several subsystems that must be present to supply the fuel cell stack or fuel cell stacks.

The fuel cell stack does not usually have a single actuator, i.e. it is a passive component or assembly on its own.

Although individual subsystems of the overall system can be well described with physical models, it is difficult to model a dynamic interaction between different subsystems and the fuel cell stack. For example, the fuel cell stack contains inertias such as thermal mass, water or moisture, which can change the dynamics of the overall system and cause direction-dependent effects such as a difference between a positive load step and a negative load step.

Disclosure of Invention

A computer-implemented method and a device according to the independent claims make it possible at one point in time to predict an operating variable of a fuel cell system at a next point in time as a function of at least one control variable.

The computer-implemented method for operating the fuel cell system provides that at least one control variable for control of the fuel cell system is specified, with a model predicting a variable of the fuel cell system depending on the at least one control variable or depending on at least one control variable set for the at least one control variable is determined, and at least one parameter of the model is determined as a function of the variable and the prediction of the variable, the at least one predetermined control variable being determined as a function of a measure of an uncertainty for the forecast of the variable by the model, for which the measure a condition for the uncertainty is fulfilled.

In one aspect, the variable is a measured value for the operating variable, the prediction of the operating variable of the fuel cell system being determined with the model as a function of the at least one control variable or as a function of at least one control variable set for the at least one control variable.

Advantageously, in another aspect, it is provided that, depending on the at least one control variable or depending on at least one control variable set for the at least one control variable, a prediction of an operating variable of the fuel cell system is determined with a first model, with the variable being a deviation of the prediction of the operating variable of the Fuel cell system from a measured value for the operating variable, the prediction of the deviation being determined as a function of the at least one control variable or as a function of at least one control variable set for the at least one control variable with a second model.

This enables improved operation of the fuel cell system depending on the prediction. An improvement for the overall system can be used, for example, for optimizing consumption, minimizing aging or degradation or extending service life, improving dynamics or performance, saving costs, for example through optimized operation. The improvement can also be used to perform further optimization with several of the previously mentioned goals, for example as adaptive multi-objective optimization.

The condition in the example is that the measure for the uncertainty is maximized. This can be done depending on a security condition, for example. The parameter can be a hyperparameter, for example for a Gaussian process. The measure of the uncertainty is an estimated uncertainty about the deviation for the set control variable. This uncertainty is, for example, by means of a probabilistic model, eg a Gaussian process. For example, the measure of uncertainty is defined by an entropy of a probability distribution of a nonlinear autoregressive exogenous Gaussian process model for time series, GP-NARX. For example, the at least one control variable that maximizes the degree of uncertainty is determined. This determines a maximally informative control variable for the training. The at least one control variable can also be determined, which maximizes the degree of uncertainty, in particular under the condition that the safety condition is met. This represents an iteration step in an iterative training with training data, in which the operating variable is predicted as a function of at least one set control variable. In iterative training, especially active learning, many iterations can be used in which the model is improved. The first model is a physical model that is based, for example, on differential equations that describe the behavior of the fuel cell system, ie the fuel cell stack or individual parts thereof. The second model is a data-based model that is intended to use a Gaussian process, for example, to predict the deviation between the physical model and the actually measured behavior of the fuel cell system. The second model trained in this way can be used after the training to correct the physical model, independently of measured values for the operating variable that were only measured during the training and are predicted by the model after the training. The operating size can be a scalar value. The condition is met by the at least one parameter, for example, if the predictive uncertainty of the model that has already been trained becomes maximum as a result of this. This at least one parameter is determined, for example, using a gradient descent method. The at least one set control variable can be a scalar value or a vector with multiple values for different control variables. The measured value for the operating variable is recorded on the fuel cell system. The operating variable is set in the fuel cell system by controlling the subsystems that supply the fuel cell stack, which is defined as a function of a requested value for the operating variable with a strategy for controlling the fuel cell system.

A sequence of the at least one set control variable within a period of time is preferably provided for the prediction of the operating variable. The sequence is defined by a time series of discrete values of the at least one set control variable. The length of the period, i.e. the time series, can be of any length. In order to reduce the computing time, a time series can preferably only include values for a previous point in time or only for a maximum of ten previous points in time.

The at least one set control variable is preferably detected with a sensor during operation of the fuel cell system. The set control variable can be precisely recorded by sensors.

Preferably, at least one third model for at least part of the fuel cell system is used to determine a prediction for at least one set control variable for at least part of the fuel cell system, depending on a predefined control variable for at least one part of the fuel cell system, with the at least one set control variable being defined as a function of the prediction is. In a real fuel cell system, a control variable specified at the first point in time is not necessarily set precisely or not immediately precisely. With the third model, the control variable that is actually set is determined as a function of the specified control variable. This lowers the costs that would otherwise be incurred for sensors and/or makes it possible to also take control variables for which no sensors are available into account.

A cost function is preferably defined as a function of the at least one control variable to be specified, with the control variable to be specified for which the cost function fulfills a condition being determined. The cost function is a measure of safety costs. For example, the measure of the cost of safety is defined by the probability that the time series is within the safe range. The condition is, for example, that the cost function for the control variable to be specified is greater than a threshold value. This means that the control variable to be specified maximizes the degree of uncertainty and satisfies a secondary condition. The constraint is, for example, that the measure of uncertainty is greater than the threshold.

The operating variable is preferably an electrical power, e.g. a terminal power of the fuel cell stack, a voltage, an efficiency or a waste heat, in particular a thermal power, of the fuel cell system. Or a derived size or substitute size.

The set control variable preferably defines a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature a coolant when it enters and a second temperature of the coolant when it exits the fuel cell system, a humidity of air, in particular when it exits from the fuel cell system, a pressure of air, hydrogen and/or coolant, an operating temperature, an air mass flow, a hydrogen molecule mass flow, a cooling medium mass flow or an electrical parameter, in particular a current, a current density or a voltage on the fuel cell system. The fuel cell stack represents the fuel cell system as an overall system with the supplying systems. The control variable defines, for example, the pressure or air mass flow in a part of the fuel cell system, which serves to supply and/or remove air. The control variable can define the hydrogen molecule mass flow in a part of the fuel cell system which serves to circulate hydrogen in the fuel cell system. The control variable can define the cooling medium mass flow of a part of the fuel cell system, which is used to cool the fuel cell system. The control variable can define the electrical characteristic of an electrical part of the fuel cell system, for example a current or a voltage of one of the fuel cells or of the fuel cell system.

Preferably, the at least one predetermined control variable defines a target value for a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature of a coolant when it enters and a second temperature of the coolant when it exits the fuel cell system, a humidity of the air in particular when it exits the fuel cell system, a target value for a pressure of air, hydrogen and/or coolant, an operating temperature, an operating temperature, an air mass flow, a hydrogen molecule mass flow, a cooling medium mass flow or an electrical parameter, in particular a current, a current density or a voltage of the fuel cell system . The control variable defines, for example, a target value for the pressure or air mass flow in a part of the overall system that is used for air supply and/or exhaust. The control variable can define the target value for the hydrogen molecule mass flow in a part of the overall system, which serves to circulate hydrogen in the fuel cell system. The control variable can define the target value for the cooling medium mass flow of a part of the overall system, which is used to cool the fuel cell system. The control variable can define the target value of the electrical characteristic of an electrical part of the overall system, for example a current or a voltage of one of the fuel cells or of the fuel cell system.

At least one operating variable of the fuel cell system is preferably determined as a function of the prediction of the operating variable and/or as a function of the prediction for the deviation, in particular after training, independently of the deviation. The deviation is an actual or measured deviation defined depending on the measured values. This means that the prediction of the operating size by the physical model is corrected by the prediction for the deviation using the data-based model.

A device for operating a fuel cell stack provides that the device is designed to carry out the method. The device comprises at least one computing device for calculating steps in the method and at least one memory for the models and can comprise one or more sensors that record the measured quantities.

• 1 eine schematische Darstellung einer Vorrichtung zum Betreiben eines Brennstoffzellensystems,
• 2 eine schematische Darstellung eines Zusammenwirkens von Modellen für das Betreiben des Brennstoffzellensystems,
• 3 Schritte in einem Verfahren zum Betreiben des Brennstoffzellensystems,
• 4 eine weitere schematische Darstellung eines Zusammenwirkens von Modellen für das Betreiben des Brennstoffzellensystems,
• 5 Schritte in einem weiteren Verfahren zum Betreiben des Brennstoffzellensystems.

Further advantageous embodiments result from the following description and the drawing. In the drawing shows

• 1 a schematic representation of a device for operating a fuel cell system,
• 2 a schematic representation of an interaction of models for the operation of the fuel cell system,
• 3 Steps in a method for operating the fuel cell system,
• 4 a further schematic representation of an interaction of models for the operation of the fuel cell system,
• 5 Steps in another method of operating the fuel cell system.

In 1 a device 100 for operating a fuel cell system with a fuel cell stack is shown schematically. The device 100 is designed to carry out a method described below. The device 100 includes a first model 101, a second model 102 and at least a third model 103. The fuel cell system includes a fuel cell stack and supplying systems. The fuel cell system forms an overall system that is at least partially modeled with the at least one third model 103 in the example. The at least one third model 103 is in the example also a chemical or physical model described in particular by differential equations.

• Ein Modell 103-1 für einen Teil des Gesamtsystems, welcher der Luftzu- und/oder abfuhr dient.
• Ein Modell 103-2 für einen Teil des Gesamtsystems, welcher der Zudosierung von Wasserstoff aus einem Tanksystem, der Abfuhr des Purgegases aus dem Anodenpfad, der Entwässerung des Anodenpfades und der Zirkulation von Wasserstoff im Brennstoffzellensystem dient.
• Ein Modell 103-3 für einen Teil des Gesamtsystems, welcher der Kühlung des Brennstoffzellensystems dient.
• Ein Modell 103-4 für einen elektrischen Teils des Gesamtsystems, welcher die elektrische Leistung des Brennstoffzellenstacks in ein Bordnetz oder ein anderes elektrisches Netz überträgt, beispielsweise mittels eines DC/DC-Wandlers und weiteren Komponenten z.B. Vorrichtung für Kurzschluss, Strommessung, Spannungsmessung des Brennstoffzellenstacks und/oder von Zellpaketen und/oder Einzelzellen des Brennstoffzellenstacks.

The following four third models 103 are shown in the example:

• A model 103-1 for a part of the overall system that is used for air supply and/or exhaust.
• A model 103-2 for part of the overall system, which is used for metering in hydrogen from a tank system, removing the purge gas from the anode path, draining the anode path and circulating hydrogen in the fuel cell system.
• A model 103-3 for a part of the overall system, which is used to cool the fuel cell system.
• A model 103-4 for an electrical part of the overall system, which transmits the electrical power of the fuel cell stack to an on-board network or another electrical network, for example by means of a DC/DC converter and other components, e.g. devices for short circuits, current measurement, voltage measurement of the fuel cell stack and / or cell stacks and / or individual cells of the fuel cell stack.

The first model 101 is designed as a physical model that describes physical relationships in the fuel cell system, for example by means of differential equations.

The second model 102 is designed as a data-based model that models a differential model between the physical model and the actual behavior of the fuel cell system.
So far, there are no precise, dynamic models that describe the behavior of the entire fuel cell system. Although individual parts of the overall system can be described well with the at least one third model 103, the dynamic interaction of these in the overall system is little or not at all known.

The aim of the modeling is therefore at a point in time t a prediction, for example, of the electrical power of the fuel cell system at a next point in time t+1 depending on possible control variables at point in time t and within a short previous time period T.

1. [1] Control Analysis of an Ejector Based Fuel Cell Anode Recirculation System, Amey Y. Karnik, Jing Sun and Julia H. Buckland.
2. [2] Model-based control of cathode pressure and oxygen excess ratio of a PEM fuel cell system, Michael A. Danzer, Jörg Wilhelm, Harald Aschemann, Eberhard P. Hofer.
3. [3] Humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static Feedback Controller, Amey Y. Karnik, Jing Sun, Fellow, IEEE, Anna G. Stefanopoulou, and Julia H. Buckland.
4. [4] MODELING AND CONTROL OF AN EJECTOR BASED ANODE RECIRCULATION SYSTEM FOR FUEL CELLS, Amey Y. Karnik, Jing Sun.
5. [5] Flachheitsbasierter Entwurf von Mehrgrößenregelungen am Beispiel eines Brennstoffzellensystems, Daniel Zirkel.
6. [6] Modellprädiktive Regelung eines PEM-Brennstoffzellensystems, Jens Niemeyer.
7. [7] Regelung zum effizienten Betrieb eines PEM-Brennstoffzellensystems, Christian Hähnel

This modeling is based on a hybrid model that has a chemical and/or physical and a data-based part. The chemical and physical part consists of parts of the overall system that are already known, for which the first model 101 and the at least one third model 103 are defined in the form of differential equations. Examples of the differential equations used, which describe the dynamic behavior of the individual parts of the overall system, in the example of the air system, the cooling system, the hydrogen system and the electrical system, are known, for example from:

1. [1] Control Analysis of an Ejector Based Fuel Cell Anode Recirculation System, Amey Y Karnik, Jing Sun and Julia H Buckland.
2. [2] Model-based control of cathode pressure and oxygen excess ratio of a PEM fuel cell system, Michael A. Danzer, Jörg Wilhelm, Harald Aschemann, Eberhard P. Hofer.
3. [3] Humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static Feedback Controller, Amey Y Karnik, Jing Sun, Fellow, IEEE, Anna G Stefanopoulou, and Julia H Buckland.
4. [4] MODELING AND CONTROL OF AN EJECTOR BASED ANODE RECIRCULATION SYSTEM FOR FUEL CELLS, Amey Y. Karnik, Jing Sun.
5. [5] Flatness-based design of multivariable controls using the example of a fuel cell system, Daniel Zirkel.
6. [6] Model predictive control of a PEM fuel cell system, Jens Niemeyer.
7. [7] Regulation for efficient operation of a PEM fuel cell system, Christian Hähnel

All of these parts of the overall system have individual manipulated variables that affect their dynamics. The manipulated variables of the fuel cell system and their description, with which the dynamics can be influenced or by which the dynamics are influenced, are listed below for exemplary parts of the overall system. These sizes are also essential for the degradation or aging of the individual components in particular of the fuel cell stack and for the energy consumption or power requirements of the systems supplying the fuel cell stack, in particular due to parasitic losses. For example, an air compressor of the fuel cell system alone can consume 15% of the fuel cell stack power. The fuel cell stack must deliver this gross power so that it can deliver a desired net power as useful power.

1) air system

lambda_cath: Excess air over stoichiometry in the cathode path of the fuel cell system. mAir_cath: Air mass flow in the cathode path of the fuel cell system. p_cath: Pressure in the cathode path of the fuel cell system. T_cath: Temperature in the cathode path of the fuel cell system. fi_cath: Humidity in the cathode path of the fuel cell system.

This part of the fuel cell system serves to supply and/or remove air for the fuel cell stack.

The variables lambda_cath and mAir_cath can be used alternatively in the example. Humidity can be used if the fuel cell system can adjust the humidity of an incoming air.

2) Hydrogen system

lambda_anod: Hydrogen molecule excess, i.e. H2 excess, relative to stoichiometry in the anode path of the fuel cell system mH2_anod: Hydrogen molecule mass flow, i.e. H2 mass flow, in the anode path of the fuel cell system p_anod: Pressure in the anode path of the fuel cell system. dp_anod_cath: Differential pressure between the cathode path and the anode path in the fuel cell system mN2_anod: Nitrogen mass flow, concentration or a nitrogen molecule flow in the anode mH2_addfromtank: H2 mass or H2 mass flow which is metered into the anode path from an H2 tank of the fuel cell system or from outside. Purge_actuation: Control for draining or removing anode gas from the anode path. Drain_actuation: Control for draining or removing liquid water from the anode path. Purge&Drain_actuation: Combined control of the valves or a common valve for Purge_actuation and Drain_actuation.

This part of the fuel cell system is used for the circulation of hydrogen and other functions for the fuel cell system.

The variables lambda_anod and mH2_anod can be used alternatively in the example. For example, a recirculation rate of a hydrogen recirculation fan is associated with mH2_anod if this is present in the fuel cell system.

The variable mH2_addfromtank can also include a temperature specification. The quantity mH2_addfromtank can be used in addition to lambda_anod or mH2_anod or in combination with it.

The variable mN2_anod can be derived from a model calculation or determined by a sensor. The mN2_anod variable can be used to trigger a purge action.

The variable Purge_actuation can specify an opening duration and/or an opening interval of a valve for the venting or removal of anode gas in a time-discrete, interval-like manner. Both can be variable.

The variable Drain_actuation can specify an opening duration and/or an opening interval of a valve for draining or removing liquid water in a time-discrete, interval-like manner. Both can be variable.

3) Cooling system

T_Stack_op: Operating temperature of coolant for the fuel cell system, i.e. approximately an operating temperature of the fuel cell system. Fan_actuation: Control of a fan dT_Stack: Temperature change of the coolant, e.g. heating, via the fuel cell system. m_Cool: Coolant mass flow through a cooling path of the fuel cell system. dp_Cool: Pressure drop across the cooling path of the fuel cell system. Pump_actuation: Pump control for generating the coolant mass flow Valve_actuation: Valve control for generating the coolant mass flow p_Cool: Pressure in the coolant path of the stack.

This part of the fuel cell system serves to circulate coolant in the fuel cell system.

The variable T_Stack_op can be expanded or used more precisely for a membrane that represents a temperature-critical component of the fuel cell stack. For this purpose, the membrane temperature can be inferred, for example, by means of a model from the coolant temperature, the stack exhaust air temperature, the stack voltage and the stack current.
The operating temperature can be modeled depending on a load, an ambient temperature, the activation of the fan, ie depending on Fan_actuation.

The variable dT_Stack can be determined as a function of a temperature difference between an outlet temperature and an inlet temperature of the coolant and can be set using a mass flow of the coolant, for example with a pump and a three-way valve of the cooling system for the fuel cell system.

As an alternative to variable p_Cool, a differential pressure to the cathode and/or to the anode can be used.

4) Electrical system

• Voltage:
• Electricity:
• current density:
• electrical power:
• Short-circuit relays, short-circuit devices and, if necessary, other electrical actuators

The electrical quantities of voltage, current, current density and electrical power of the fuel cell stack interact strongly with a power network, the architecture of which can be very different.

For example, the electrical power of the fuel cell stack can be transmitted from the fuel cell stack to the power grid by means of a DC converter, e.g. DC/DC converter, depending on a voltage and/or a current. For example, the DC/DC converter can adjust the current drawn from the fuel cell stack via a voltage gradient.

A shorting relay can be provided which shorts the fuel cell stack, i.e. both terminals. This can be used, for example, for a freeze start, in which at times no electrical power is supplied to a power grid, but the electrical power is converted into heat.

Variables derived from this, e.g. resistance or efficiency, can also be modeled.

These quantities represent variables. Not all possible variables are exhaustively listed. Each variable can have a model-based value and a measured value. In addition or as an alternative to absolute variables, differential variables or differences from reference values can also be used. Only a subset of the possible variables can also be used as parameters for the modelling.

The device 100 includes a control device 104, which is designed to control the fuel cell system or the subsystems for operating the fuel cell stack with the individual manipulated variables. The device 100 can include a measuring device 106, in particular a sensor for detecting variables on the fuel cell system. In the example, the device comprises at least one computing device 108, which is designed to carry out steps in a method described below, and at least one memory 110 for the models. The at least one computing device 108 can be a local computing device in a vehicle, a computing device on a server or in the cloud, or a computing device distributed in particular across a plurality of servers or the vehicle and at least one server.

Based on 2 an interaction of the models for the operation of the fuel cell system is described.

In the example, an operating variable y_req to be provided is defined as an input variable for the fuel cell system. This operating variable is preferably electrical power, voltage, efficiency or waste heat, in particular thermal power, of the fuel cell system. The fuel cell system should be controlled with at least one control variable u_req in such a way that the fuel cell actually provides this operating variable. This at least one control variable u_req represents a target value for the control of the fuel cell system by control device 104. In the example, the operating variable y_req to be provided is mapped to the at least one control variable u_req by a strategy for the control. The strategy can be a mapping of the operating variable y_req to be provided by a predefined linear or non-linear function or by a predefined table onto the at least one control variable u_req.

Due to dead times, inertia, hysteresis, aging effects or deviations from the setpoint of the actuators, a control variable that deviates from the setpoint can occur. On the one hand, this can be detected by a sensor, for example, as the control variable u_act that is actually set. On the other hand, the at least one set control variable u_pred can be determined as a prediction using the at least one third model 103. In the example, for at least part of the fuel cell system, in particular for the fuel cell stack or for at least one of the subsystems for its supply, a prediction x[subsy]_pred for the at least one set control variable u_pred determines at least part of the fuel cell system and defines the at least one set control variable u_pred depending on the prediction x[subsy]_pred. In the example, the variables x[subsy]_req are combined in a vector that defines the control variable u_req. Each of the control variables listed above can be used as a variable x[subsy]_req for the respective part of the fuel cell systems are used. If several manipulated variables are provided for a part, the variable x[subsy]_req represents a vector that includes these manipulated variables. Only selected sizes are described below as examples.

In 2 are the quantities for the model 103-1, i.e. for the air system, denoted by [subsy] = A, the quantities for the model 103-2, i.e. for the hydrogen system, with [subsy] = H, the quantities for the model 103 -3, ie for the cooling system, with [subsy] = C and the sizes for the model 103-4, ie for the electrical system, with [subsy] = E.

All or only parts of the actual control variables can be determined or measured with the model depending on the respectively specified control variable.

Regardless of whether the set control variable is measured, u_act, or modeled, u_pred, this can be a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature of a coolant when it enters and a second temperature of the coolant when it exits from the fuel cell system, air humidity, in particular when it exits the fuel cell system, air, hydrogen and/or coolant pressure, operating temperature, air mass flow, hydrogen molecule mass flow, cooling medium mass flow or an electrical parameter, in particular a current, a current density or a voltage at the fuel cell system. The fuel cell system represents an overall system.

The control variable defines, for example, a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature of a coolant when it enters and a second temperature of the coolant when it exits the fuel cell system, a humidity of the air in particular when it exits the fuel cell system , the pressure of air, hydrogen and/or coolant, an operating temperature or air mass flow in a part of the fuel cell system, which is used for air supply and/or discharge. The set control variable can define the hydrogen molecule mass flow in that part of the fuel cell system which serves to circulate hydrogen in the fuel cell system. The control variable can define the cooling medium mass flow of a part of the fuel cell system, which is used to cool the fuel cell system. The set control variable can define the operating temperature, which is approximately a coolant temperature. The set control variable can define the electrical characteristic of an electrical part of the fuel cell system, for example a current, a current density or a voltage of one of the fuel cells or of the fuel cell system.

The at least one predefined control variable u_req preferably defines the setpoint for the pressure, the operating temperature, the air mass flow, the hydrogen molecule mass flow, the cooling medium mass flow or the electrical parameter, in particular the current or the voltage of the fuel cell system. In the example, the control variable xA_req defines at a point in time t a setpoint value for the pressure or air mass flow in the part of the overall system that is used for air supply and/or exhaust. In the example, at time t, control variable xH_req defines a target value for the hydrogen molecule mass flow in that part of the overall system that serves to circulate hydrogen in the fuel cell system. In the example, at time t, control variable xC_req defines the target value for the cooling medium mass flow of that part of the overall system that is used to cool the fuel cell system. The control variable can also define the operating temperature, which is approximately the coolant temperature. In the example, the control variable xE_req defines the setpoint value of the electrical parameter of the electrical part of the overall system at time t, for example the current or the voltage of the fuel cells or of the fuel cell system. In the example, the specified control variable u_req is a vector u_req=(xA_req, xH_req, xC_req, xE_req) ^τ . Accordingly, the control variable that is set is defined by a vector in the example. In the event that all control variables that arise are measurable, the control variable that arises is u_act=(xA_act, xH_act, xC_act, xE_act) ^τ . In the event that all control variables that arise are modeled, the control variable that arises is u_pred=(xA_pred, xH_pred, xC_pred, xE_pred) ^τ . Mixed forms are preferably used in which the control variables that are measurable with sensors that are available in any case on the fuel cell system are measured and the others are modeled.

An operating variable y_act of the fuel cell system is determined by the first model 101 as a function of the at least one control variable that is set. In the example, the operating variable that is set is a scalar, but a vector with multiple values of different operating variables can also be determined by the first model 101 . In the example, for the first model 101 is used as stationary-Mo dell uses the Kulikovsky fuel cell model. The Kulikovsky model was derived analytically from the underlying differential equation system for describing the electrokinetics of the cathode catalyst layer. This model uses the input variables cathode mass flow, cathode lambda, cathode inlet pressure, cathode outlet pressure, humidity at the cathode inlet, humidity at the cathode outlet, current or current density, coolant inlet temperature, coolant outlet temperature.

Depending on the at least one control variable that is set, second model 102 determines a prediction for a deviation dy_pred of operating variable y_act determined by first model 101 from an actual value of the operating variable in the fuel cell system. The actual value, i.e. a measured operating variable y_mes, is determined for training. The measured operating variable y_mes is measured in the vehicle during training, for example on a test bench, or online, i.e. during operation of a vehicle. During training, an actual deviation dy is determined in a comparison device 201 as a function of the measured operating variable y_mes and the operating variable y_act determined by the first model 101 .

In the example, the second model 102 is the data-based model that is intended to use the Gaussian process to predict a deviation dy_pred between the first model 101 and the actually measured behavior of the fuel cell system. During training, the second model 102 can initially be randomly initialized and trained in iterations as described below.

The second model 102 can already be trained. In this case, the measurement of the measured operating variable y_mes and the determination of the actual deviation dy can be omitted.

An operating variable y_pred is determined at a correction device 202 as a function of the operating variable y_act determined by the first model 101 and of the prediction for the deviation dy_pred. This means that the prediction of the operating size by the physical model is corrected by the prediction for the deviation using the data-based model.

During training, computing device 108 determines at least one parameter P for first model 101 and/or second model 102. In the example, the at least one parameter P is dependent on the at least one control variable u_req, the at least one control variable that is set, ie the measured control variable u_act and/or the modeled control variable u_pred, the prediction for the deviation dy_pred and the deviation dy. This is described below.

The following with reference to 3 The computer-implemented method described for operating a fuel cell system provides in a step 301 that at least one control variable u_req is specified for a control of the fuel cell system. During training, the at least one control variable u_req is determined independently of the strategy as a function of a measure of an uncertainty h(u_req) for predicting the operating variable y_pred of the fuel cell system by first model 101 using the following procedure. In the example, a time series of the set control variables u_act(t) of the subsystems for times t = 1...T or the modeled set control variables u_pred(t) from the calculated prediction for the subsystems x[subsys]_pred(t) for times is used t = 1..T used.

The at least one predefined control variable u_req for which the measure for the uncertainty h(u_req) satisfies a condition is determined for the measure for the uncertainty h(u_req).

The measure of the uncertainty is an estimated uncertainty about the control variable that is actually set. This uncertainty is determined, for example, using a probabilistic model, e.g. a Gaussian process. For example, the measure of uncertainty is defined by an entropy of a probability distribution of a nonlinear autoregressive exogenous Gaussian process model for time series, NARX.

In the example, at a point in time t, the at least one control variable u_req is determined as at least one control variable u_req(t) to be specified, which maximizes the measure for the uncertainty. This determines a maximally informative control variable for the training. The at least one control variable that maximizes the measure of the uncertainty under a secondary condition can also be determined. This constraint can be a safety constraint.

In one aspect, a cost function s(u_req(t)) is defined as a function of the at least one control variable u_req(t) to be specified. In this case, the control variable u_req(t) to be specified is determined, for which the cost function s(u_req(t)) satisfies a condition c. In the example, the cost function is a measure of safety costs. For example, the measure for the safety costs is defined by the probability given by a Gaussian process model, for example, that a time series that is determined for the control variable u_req(t) to be specified is in a safe range for the operation of the fuel cell system. The condition c is, for example, that the cost function s(u_req(t)) for the control variable u_req(t) to be specified is greater than a threshold value c. This means that the control variable u_req(t) to be specified maximizes the measure of the uncertainty h(u_req(t)) and satisfies a secondary condition s(u_req(t)) > c.

1. a) Basierend auf physikalischem Wissen mit einer Menge an Nebenbedingungen, die alle erfüllt sein müssen,
2. b) Basierend auf physikalischem Wissen mit einer einzigen Nebenbedingung, die alle sicherheitsrelevanten Aspekte zusammenfasst,
3. c) Basierend auf datenbasierten machine learning Modellen, wie in a) jeweils eines pro sicherheitsrelevantem Aspekt,
4. d) Basierend auf einem datenbasierten machine learning Modell, das wie in b) alle sicherheitsrelevanten Aspekte zusammenfasst,
5. e) Basierend auf einer Kombination aus zusammenfassenden und einzelnen Kriterien, die jeweils auf physikalischem Wissen oder machine learning Modellen basieren.

The constraint for safety, ie the safety costs, can be defined in the following way:

1. a) Based on physical knowledge with a set of constraints, all of which must be satisfied,
2. b) Based on physical knowledge with a single constraint summarizing all safety-related aspects,
3. c) Based on data-based machine learning models, as in a) one for each security-related aspect,
4. d) Based on a data-based machine learning model that summarizes all security-related aspects as in b),
5. e) Based on a combination of summary and individual criteria, each based on physical knowledge or machine learning models.

Provision can be made, for example, to evaluate or diagnose a state of a cell membrane in the fuel cell system via an impedance measurement. The impedance measurement corresponds to a sensor that can evaluate an operation or a quality of operation using an impedance spectrum. The impedance measurement can use a signal with a frequency that does not disturb the operation of the fuel cell system and provides a quality measure that results from a total of all stack operating variables, but cannot be traced back separately to individual manipulated variables. The machine learning model can be trained to use this signal as a measure of robust operation or as a safety measure or quality measure for the cell membrane.

The latter represents a hybrid model. The machine learning model or models can each be regression or classification models.

• Ausgehend von einer Zeitserie u_req(t) = u_req(t-1), ... u_req(t-T) und einem dafür bekannten gemessenen Wert der Betriebsgröße y_mes(t) wird zunächst eine Abweichung dy(t) bestimmt. Für einen Approximation der Abweichung dy(t) durch das zweite Modell 102 ist für eine Eingabe x mit einer Mittelwertfunktion µ(x) und einer Kovarianzfunktion k(x_i_x_j) ein Gaußprozess GP definiert, welcher der Eingabe x_i = u_req(t-1), ... u_req(t-T) eine Ausgabe dy_pred(t) = f(x_i) = GP(µ(x_i),k(x_i, x_j)) zuordnet. Für die Zeitserie u_req(t) = u_req (t-1), ... u_req(t-T) als Eingabe x_i wird als Ausgabe dy_pred(t) = f(x_i) die Vorhersage für die Abweichung dy_pred(t) zugeordnet.

To determine the control variable u_req(t) to be specified, the following is carried out in the example:

• Based on a time series u_req(t)=u_req(t-1), ... u_req(tT) and a known measured value of the operating variable y_mes(t), a deviation dy(t) is first determined. For an approximation of the deviation dy(t) by the second model 102, a Gaussian process GP is defined for an input x with a mean value function µ(x) and a covariance function k(x_i_x_j), which corresponds to the input x_i = u_req(t-1), ... u_req(tT) assigns an output dy_pred(t) = f(x_i) = GP(µ(x_i),k(x_i, x _j )). For the time series u_req(t) = u_req (t-1), ... u_req(tT) as input x_i, the prediction for the deviation dy_pred(t) is assigned as output dy_pred(t) = f(x_i).

In the example, a Gaussian kernel is used as the covariance function k(x_i, x_j) and the mean value is zero for this Gaussian process.

For the training, a control variable u_req(t+1) to be specified should be determined for which the prediction of the deviation dy_pred(t+1) offers the greatest possible information gain with regard to the assignment of input x to output f(x) by the Gaussian process. The measure for the uncertainty h(u_req) and the secondary condition according to which the cost function s(u_req) must fulfill condition c are used for this purpose. In the example, the threshold value C is used to determine a control variable u_req (t+1) to be specified as $$\text{Max}\_\left\{\text{and}\_\text{req}\right\}\text{H}\left(\text{and}\_\text{req}\right)\text{where s}\left(\text{and}\_\text{req}\right)>\text{C}.$$

Here, h(u_req)=σ(u_req) can be chosen, where σ(u_req) is the predictive variance of the Gaussian process trained on the data.
In particular, the safety condition can be determined by a further Gaussian process GP_{saf}, with a predictive mean µ_{saf}(u_req(t)) at the points u_{req}(t) and a predictive covariance σ_{saf}(u_{req}( t)) be defined. Then the cost function s(u_req) is defined as $$\begin{array}{l}\text{s}\left(\text{and}\_\left\{\text{req}\right\}\left(\text{t}\right)\right)=\backslash \text{internal}\_\left\{\text{s}1>\mathrm{0,}...,\text{sT}>0\right\}\backslash \text{mathcal}\left\{\text{N}\right\}(\text{s}\mathrm{1,}...,\text{sT}|\backslash \text{mu}\_\left\{\text{safe}\right\}\left(\text{and}\_\text{req}\left(\text{t}\right)\right),\\ \backslash \text{Sigma}\_\left\{\text{safe}\right\}\left(\text{and}\_\left\{\text{req}\right\}\left(\text{t}\right)\right)).\end{array}$$

Subsequently, in a step 302, depending on the at least one control variable u_req or depending on at least one control variable set for the at least one control variable u_req(t), i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred, with the first model 101 the prediction of the operating variable y_act of the fuel cell system is determined.

Subsequently, in a step 303, the deviation dy of the prediction of the operating variable y_act of the fuel cell system from the measured value y_mes for the operating variable is determined.

A sequence of the at least one set control variable, i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred, is preferably provided within a time period T for the prediction of the operating variable y_act. The sequence is defined by a time series of discrete values of the at least one set control variable, i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred. The length of the period, i.e. the time series, can be of any length. In order to reduce the computing time, a time series can preferably only include values for a previous point in time or only for a maximum of ten previous points in time. The at least one set control variable u_act is preferably detected with a sensor during operation of the fuel cell system.

Subsequently, in a step 304, depending on the at least one control variable u_req or depending on at least one control variable set for the at least one control variable u_req(t), i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred, with the second model 102 the prediction dy_pred of the deviation dy is determined.

Then, in a step 305, the at least one parameter P of the first model 101 and/or the second model 102 is determined as a function of the deviation dy and the prediction dy_pred of the deviation dy.

Step 301 is then executed.

The steps represent an iteration in an iterative training with training data, in which the operating variable is predicted as a function of at least one predetermined or set control variable. In the case of iterative training, in particular active learning, many iterations can be used in which the first model 101 and/or the second model 102 is improved. After the training, the second model trained in this way can be used to correct the physical model, independently of measured values for the company variable.

In this case, after the training, in a step 306, the at least one control variable u_req is determined using the strategy as a function of the operating variable y_req to be set. The strategy is defined in the example.

Subsequently, in a step 307, depending on the at least one control variable u_req or depending on at least one control variable set for the at least one control variable u_req(t), i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred, with the first model 101 the prediction of the operating variable y_act of the fuel cell system is determined.

Subsequently, in a step 308, depending on the at least one control variable u_req or depending on at least one control variable set for the at least one control variable u_req(t), i.e. in the example the measured control variable u_act and/or the modeled control variable u_pred, with the second model 102 the prediction dy_pred of the deviation dy is determined.

Subsequently, in a step 309, the corrected operating variable y_pred is determined as a function of the prediction of the operating variable y_act and the forecast dy_pred of the deviation dy.

Step 306 is then executed.

The method ends, for example, after training or when the fuel cell system is switched off.

In one aspect, the method can be carried out independently of the first model 101 . This is based on the 4 and the 5 described.

As in 4 shown schematically, the actual deviation dy is determined in contrast to the previously described procedure with the comparison device 201 depending on the measured value y_mes and a prediction of the second model 102 for the corrected performance variable y_pred. The first model 101 and the prediction y_act of the farm size are not used. Otherwise, the models interact as previously described. In 4 the same reference numerals denote elements having the same function as for 3 described.

In contrast to the method described above, the procedure is as follows.

In a step 501, as described for step 301, the at least one control variable u_req is specified for control of the fuel cell system.

The aspects of the first model 101 described in steps 302 and 303 are not carried out in this aspect.

In a subsequent step 502, the procedure is as described for step 304, in contrast to this depending on the at least one control variable u_req or depending on at least one control variable u_act, u_pred set for the at least one control variable u_req(t) with the second model 102 the corrected performance variable y_pred is determined. The corrected operating variable y_pred is a prediction of the measured value y_mes of the fuel cell system.

Subsequently, in a step 503, the deviation dy of the corrected operating variable y_pred of the fuel cell system from the measured value y_mes for the operating variable is determined.

In a subsequent step 504, the procedure is as described for step 305, with the difference being that the at least one parameter P of the model 102 is determined as a function of the measured value y_mes and the prediction y_pred.

This means that in step 501 the procedure is as described for step 301, in contrast to this, depending on the measure of the uncertainty h(u_req) for the corrected operating variable y_pred, ie for the prediction of the measured variable y_mes by the second model 102, the at least one predetermined control variable u_req determined for which the measure of the uncertainty h(u_req) satisfies the condition.

Steps 501 to 504 can be repeated for training.

A step 505 is then carried out with the second model 102 trained in this way, as described for step 306 .

Subsequently, a step 506 as described for step 307 is executed.

Subsequently, a step 507 as described for step 308 is executed.

A step 508 as described for step 309 is then executed.

Steps 505 through 508 can be repeated.

The method ends, for example, after training or when the fuel cell system is switched off.

Claims (13)

Computer-implemented method for operating a fuel cell system , characterized in that at least one control variable (u_req) for control of the fuel cell system is specified (301, 501), depending on the at least one control variable (u_req) or depending on at least one for the at least one control variable ( u_req(t)) set control variable (u_act, u_pred) with a model (102) a prediction (y_pred, dy_pred) of a variable (y_mes, dy) of the fuel cell system is determined (304, 502), and depending on the variable (y_mes , dy) and the prediction (y_pred, dy_pred) of the variable (y_mes, dy) at least one parameter (P) of the model (102) is determined (305, 504), depending on a measure of an uncertainty (h(u_req) ) for the prediction (y_pred, dy_pred) of the variable (y_mes, dy) by the model (102), the at least one predetermined control variable (u_req) is determined (301, 501), for which the measure of the uncertainty (h(u_req) ) one e condition fulfilled. procedure after claim 1 , characterized in that the variable (y_mes) is a measured value (y_mes) for the operating variable, the prediction (y_pred) of the operating variable of the fuel cell system depending on the at least one control variable (u_req) or depending on at least one for the at least one control variable ( u_req(t)) set control variable (u_act, u_pred) is determined with the model (102) (502). procedure after claim 1 , characterized in that a prediction of an operating variable (y_act ) of the fuel cell system is determined (302), the variable (dy) being a deviation (dy) of the prediction of the operating variable (y_act) of the fuel cell system from a measured value (y_mes) for the operating variable (303), depending on the at least one control variable (u_req) or depending on at least one control variable (u_act, u_pred) set for the at least one control variable (u_req(t)) with a second model (102) the prediction (dy_pred) of the deviation (dy) is determined (304). Method according to one of the preceding claims, characterized in that a sequence of the at least one set control variable (u_act, u_pred) within a time period (T) is provided for the prediction of the operating variable (y_act, y_pred). Method according to one of the preceding claims, characterized in that the at least one set control variable (u_act) is detected with a sensor during operation of the fuel cell system. Method according to one of the preceding claims, characterized in that a prediction (x[subsy ]_pred) is determined for at least one set control variable (u_pred) for at least part of the fuel cell system, the at least one set control variable (u_pred) being defined as a function of the prediction (x[subsy]_pred(t)). Method according to one of the preceding claims, characterized in that a cost function is defined as a function of the at least one control variable (u_req) to be specified, the control variable (u_req) to be specified being determined for which the cost function fulfills a condition (c) (301, 501 ). Method according to one of the preceding claims, characterized in that the operating variable is electrical power, voltage, efficiency or waste heat, in particular thermal power, of the fuel cell system. Method according to one of the preceding claims, characterized in that the set control variable (u_act, u_pred) a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature of a coolant when it enters and a second temperature of the coolant when it exits from the fuel cell system, a humidity of air, in particular when it exits the fuel cell system, a pressure of air, hydrogen and/or coolant, an operating temperature, an air mass flow, a water substance molecular mass flow, a cooling medium mass flow or an electrical parameter, in particular a current, a current density or a voltage in the fuel cell system. Method according to one of the preceding claims, characterized in that the at least one predetermined control variable (u_req) is a target value for a pressure difference between an anode and a cathode of the fuel cell system, a temperature difference between a first temperature of a coolant at its inlet and a second temperature of the coolant when it exits the fuel cell system, a humidity of the air, in particular when it exits the fuel cell system, a target value for a pressure of air, hydrogen and/or coolant, an operating temperature, an air mass flow, a hydrogen molecule mass flow, a cooling medium mass flow or an electrical parameter, in particular one Current, a current density or a voltage of the fuel cell system is defined. Method according to one of the preceding claims, characterized in that at least one operating variable (y_act) of the fuel cell system is dependent on the prediction of the operating variable (y_pred) and/or dependent on the prediction for the deviation (dy_pred), in particular after training, independently of the deviation ( dy) is determined. Device for operating a fuel cell system , characterized in that the device is designed, the method according to any one of Claims 1 until 11 to execute. Computer program, characterized in that the computer program comprises machine-readable instructions, when executed by a particular distributed computer, the method according to one of Claims 1 until 11 expires.

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